Kwon-Hee Lee

Robust optimization considering tolerances of design variables

Abstract Optimization techniques have been applied to versatile engineering problems for reducing manufacturing cost and for automatic design. The deterministic approaches of optimization neglect the effects from uncertainties of design variables. The uncertainties include variation or perturbation such as tolerance band. At optimum, the constraints must be satisfied within the tolerance ranges of the design variables. The variation of design variables can also give rise to drastic change of performances. The two issues are related to constraint feasibility and insensitive performance. Robust design suggested in the present study has been developed to obtain an optimum value insensitive to variations on design variables within a feasible region. This is performed by using a mathematical programming algorithm. A multiobjective function is defined to have the mean and the standard deviation of the original objective function, while the constraints are supplemented by adding a penalty term to the original constraints. This method has an advantage in that the second derivatives of the constraints are not required. Several standard problems for structural optimization are solved to check the usefulness of the suggested method.

Robust design for unconstrained optimization problems using the Taguchi method

Engineering optimization has been developed for the economic design of engineering systems. The conventional optimum is determined without considering noise factors. Thus, applications to practical problems may be limited. Within current design practice, noises tend to be allowed for by specification of closer tolerances, or the use of safety factors. However, these approaches may be economically infeasible. Thus, the inclusion of design-variable noises is required for practical design in optimization. A method is developed to find robust solutions for unconstrained optimization problems. The method is applied to problems with discrete variables. The orthogonal array based on the Taguchi concept is utilized to arrange the discrete variables. Through several examples, it is verified that the solutions from the suggested method are more insensitive to noise than the conventional optimum within the range of variations for design variables.

Robust optimization in discrete design space for constrained problems

Robust design in discrete design space is defined as a discrete design that is insensitive to external uncertainties or variations. The application of robust discrete design is not prevalent yet due to high computational cost. A relatively simple method is proposed to select discrete and robust optimum. At first, the discrete design is achieved as the postprocess of conventional optimization. An orthogonal array is established around a conventional optimum, and the characteristic functions are evaluated. The characteristic function is defined by considering the robustness of the objective and constraints. The parameter design of the Taguchi method is introduced to obtain the robust solution in discrete space. The present method has insensitive performance to variations of the design variables within the selected discrete values enhancing the feasibility of constraints. To enhance feasibility, ranking the estimators of the characteristic function is developed. Several structural problems are solved to show the usefulness of the present method.

An optimization algorithm using orthogonal arrays in discrete design space for structures

Structural optimization has been carried out in continuous or discrete design space. Methods for discrete design such as genetic algorithms are extremely expensive in computational cost. In this research, an iterative optimization algorithm using orthogonal arrays is proposed for design in discrete space. An orthogonal array is selected on a discrete design space and levels are chosen from candidate values. Matrix experiments with the orthogonal array are conducted. A characteristic function is defined to consider the constraint feasibility. A new design in a certain iteration is determined from analysis of means (ANOM) with the characteristic function. An orthogonal array is defined around the new values and matrix experiments are conducted again with the new orthogonal array. The final optimum design is found from the iterative process. Various structural problems are solved to show the validity of the proposed method. The results are compared with those from a genetic algorithm and discussed.

Automotive door design using structural optimization and design of experiments

Abstract Currently, the ultralight steel auto body (ULSAB) concept is receiving more attention owing to various benefits in automotive body design. One of the tasks of the ULSAB is constructing a door using tailor welded blanks (TWBs). In TWBs, two or more gauges of steel panels (parts) are welded together before the stamping process. In this research, the domains and thicknesses of the gauges in a front door structure are determined by a series of optimization methods such as topology, size and shape optimizations and design of experiments (DOE). The door is designed to have better performance compared with an existing structure in terms of stiffness and natural frequency. The final design is discussed and compared with the current design.

Optimization of an automotive side door beam, considering static requirement

Abstract Door stiffness is one of the important factors in side impact. A side door beam is installed in the door to protect occupants from side impact. Generally, side impact performance has been calculated with the assembled door unit or the body-in-white (BIW) system. Thus, the effects of a side door beam should be investigated after a BIW system is designed. This research concentrates on the side door beam, which will be optimized. The cross-section of a side door beam is defined to have an elliptic shape. An optimization problem is formulated to find the design maximizing the crush stiffness within the specified weight. Design variables are the radii and the thickness of the side door beam with the elliptic section. Analysis of the side impact is carried out by the non-linear finite element method. The optimization problem is solved by two methods. One is the experimental design scheme using an orthogonal array. The other is optimization using the response surface method (RSM). Both methods have obtained better designs than the current one.

A Global Robust Optimization Using the Kriging Based Approximation Model

A Global Robust Optimization Using the Kriging Based Approximation Model Kwon-Hee Lee, Gyung-Jin Park and Won-Sik Joo Corresponding author, Assistant Professor, Dept. of Mechanical Engineering, Dong-A University, Busan, Korea, 840 Hadan2-Dong, Busan 604-714, Korea E-mail) leekh@donga.ac.kr, Fax) +82-51-200-7656, Phone) +82-51-200-7638 Professor, Dept. of Mechanical Engineering, Hanyang University, Ansan City, Gyeonggi-Do, 426-791, Korea Professor, Dept. of Mechanical Engineering, Dong-A University, Busan, Korea, 840 Hadan2-Dong, Busan 604-714, Korea

Truss optimization considering homologous deformation under multiple loadings

The deformation of a structure shall be called homologous, if a given geometrical relation holds for a given number of structural points before, during, and after the deformation. Some researchers have utilized the idea of structural design with the finite element method. The approaches use the decomposition of the FEM equation or equality equations to obtain homologous deformation. However, weight reduction and response constraints such as stress, displacement or natural frequency cannot be considered by those theories. An optimization method solving the above problems is suggested for obtaining homologous deformation. Homology constraints can be considered under multiple loading conditions as well as a single loading condition. A homology index is defined for multiple loading conditions. Examples are solved to demonstrate the performance of the method.

A Review of Robust Design Methodologies

Robust design has been developed with the expectation that an insensitive design can be realized. That is, a product designed by robust design should be insensitive to external noises or tolerances. Robust design can be classified into three methods: (1) The Taguchi method (2) robust optimization (3) robust design by the axiomatic approach. In this paper, each method is reviewed and investigated. Pros and cons fur each method are discussed and a future direction for development is proposed.

Robust structural optimization using design axioms in a discrete design space

The design axioms provide a general framework for design methodologies. The axiomatic design framework has been successfully applied to various design tasks. However, the axiomatic design is rarely utilized in the detailed design process of structures when the optimization technology is carried out. The relationship between the axiomatic design and optimization is investigated and the logical decomposition method is developed for a systematic structural optimization. The entire optimization process is modified to satisfy the independence axiom. In the decomposition process, design variables are grouped according to sensitivities derived from the analysis of variance (ANOVA). After an optimization is conducted for the decomposed problems, the robust design using the Taguchis concept is applied for the postprocess of the mathematical optimization. The developed method is verified by examples such as the twenty-five member transmission tower and the twobay-six-story frame.